Method and apparatus for optimizing fragmentation of boundaries for optical proximity correction (OPC) purposes

ABSTRACT

The present invention is directed to a method and apparatus for optimizing fragmentation of integrated circuit boundaries for optical proximity correction (OPC) purposes. The present invention may balance the number of vertices and the “flexibility” of the boundary and may recover fragmentation according to the process intensity profile along the ideal edge position to obtain the best decision for OPC.

CROSS-REFERENCE TO RELATED DOCUMENTS

The present application is a divisional of U.S. patent application Ser. No. 10/739,460, filed Dec. 18, 2003, now U.S. Pat. No. 6,988,260, which is herein incorporated by reference in its entirety. The present application herein incorporates the following by reference in their entirety: (1) U.S. patent application Ser. No. 09/879,664, entitled “Mask Correction for Photolithographic Processes”, filed Jun. 12, 2001; and (2) N. Cobb, “Fast Optical and Process Proximity Correction Algorithms for Integrated Circuit Manufacturing,” Ph.D. Thesis, Department of Electrical Engineering and Computer Sciences, University of California at Berkeley, May 1998.

FIELD OF THE INVENTION

The present invention generally relates to the field of integrated circuits, and particularly to a method and apparatus for optimizing fragmentation of boundaries for optical proximity correction (OPC) purposes.

BACKGROUND OF THE INVENTION

With the advance of technology in integrated circuits (ICs), the minimum feature sizes of ICs have been shrinking for years. Commensurate with this size reduction, various process limitations have made IC fabrication more difficult. One area of fabrication technology in which such limitations have appeared is photolithography. Photolithography involves selectively exposing regions of a resist coated silicon wafer to a radiation pattern, and then developing the exposed resist in order to selectively protect regions of wafer layers (e.g., regions of substrate, polysilicon, or dielectric).

An integral component of a photolithographic apparatus is a “mask” or “reticle” which includes a pattern corresponding to features at one layer in an IC design. Such reticle may typically include a transparent glass plate covered with a patterned light blocking material such as chromium. The reticle may be placed between a radiation source producing radiation of a pre-selected wavelength and a focusing lens which may form part of a “stepper” apparatus. Placed beneath the stepper may be a resist covered silicon wafer. When the radiation from the radiation source is directed onto the reticle, light may pass through the glass (regions not having chromium patterns) and project onto the resist covered silicon wafer. In this manner, an image of the reticle may be transferred to the resist. The resist (sometimes referred to as a “photoresist”) is provided as a thin layer of radiation-sensitive material that is spin-coated over the entire silicon wafer surface.

As light passes through the reticle, the light may be refracted and scattered by the chromium edges. This may cause the projected image to exhibit some rounding and other optical distortion. While such effects pose relatively little difficulty in layouts with large feature sizes (e.g., layouts with critical dimensions above about 1 micron), the effects may not be ignored in layouts having features smaller than about 1 micron. The problems become especially pronounced in IC designs having feature sizes near the wavelength of light used in the photolithographic process. Optical distortions commonly encountered in photolithography may include rounded corners, reduced feature widths, fusion of dense features, shifting of line segment positions, and the like. Unfortunately, any distorted illumination pattern may propagate to a developed resist pattern and ultimately to IC features such as polysilicon gate regions, vias in dielectrics, and the like. As a result, the IC performance may be degraded or the IC may become unusable.

To remedy this problem, a reticle correction technique known as optical proximity correction (“OPC”) has been developed. Optical proximity correction may involve adding regions to and/or subtracting regions from a reticle design at locations chosen to overcome the distorting effects of diffraction and scattering. Typically, OPC is performed on a digital representation of a desired IC pattern. First, the digital pattern may be evaluated with software to identify regions where optical distortion will result. Then the optical proximity correction may be applied to compensate for the distortion. The resulting pattern may be ultimately transferred to the reticle glass. OPC may add various “corrections” to base features. For example, some correction may take the form of “serifs,” which are small appendage-type addition or subtraction regions typically made at corner regions on reticle designs. These “serifs” may have the intended effect of “sharpening” the corners of the illumination pattern on the wafer surface.

With OPC, the boundary of an IC design often needs to be moved and/or distorted. In order to get a better correction, it is often useful to introduce more vertices on the boundary to give the IC designer more freedom to design the IC. However, as the number of the vertices grows, the complexity of the masks (thus the cost) may grow. In addition, during the OPC process the fragment of the boundary edge often moves at an essential distance from its initial position, resulting in more complex structure with higher density than the initial design. This may cause different process intensity.

Therefore, it would be desirable to provide a method and apparatus for optimizing fragmentation of boundaries for OPC purposes, which may balance the number of vertices and the “flexibility” of the boundary and may recover fragmentation according to the process intensity profile along the ideal edge position to obtain the best decision for OPC.

SUMMARY OF THE INVENTION

Accordingly, the present invention is directed to a method and apparatus for optimizing fragmentation of boundaries for optical proximity correction (OPC) purposes. The present invention may balance the number of vertices and the “flexibility” of the boundary and may recover fragmentation according to the process intensity profile along the ideal edge position to obtain the best decision for OPC.

In an exemplary aspect of the present invention, a method for optimizing fragmentation of integrated circuit boundaries for optical proximity correction (OPC) purposes may include the following steps: (a) providing a segment S of an integrated circuit boundary and a neighborhood of the integrated circuit boundary as input, the segment S having a first end B and a second end E; (b) placing elements (B,0) and (E,0) into a set Ms, an element in the set Ms having a first component representing a point on the segment S and a second component representing a numeric value; (c) when a length of the segment S is not less than (D_(min)+2·D_(serif)), placing elements (B_(serif),0) and (E_(serif),0) into the set Ms, wherein B_(serif) is a beginning serif point on the segment S with a distance between B and B_(serif) being equal to D_(serif), E_(serif) is an end serif point on the segment S with a distance between E and E_(serif) being equal to D_(serif), D_(serif) is a serif size for the segment S, and D_(min) is a minimal allowed distance between any two fragmentation points on the segment S; (d) projecting at least one vertex, other than B and E, of the integrated circuit boundary and the neighborhood to the segment S to form at least one projection point P with a corresponding distance D between a vertex and the segment S; (e) when P lies on the segment S, adding an element (P,D) to the set Ms; (f) when an element (P′,D′) of the set Ms is such that a distance between the point P′ and the point B or between the point P′ and the point E is less than D_(min), and when the point P′ is neither the point B nor the point E, removing the element (P′,D′) from the set Ms; (g) when the element (B_(serif),0) is in the set Ms, when an element (P_(i), D_(i)) of the set Ms is such that the point P_(i) lies between B and B_(serif), and when another element (P_(i)′, D_(i)′) of the set Ms is such that a distance between the point P_(i)′ and the end B_(serif) is less than D_(min), removing the element (B_(serif),0) from the set Ms; (h) when the element (E_(serif),0) is in the set Ms, when an element (P_(i)″,D_(i)″) of the set Ms is such that the point P_(i)″ lies between E and E_(serif), and when another element (P_(i) ′″, D_(i)′″) of the set Ms is such that a distance between the point P_(i)′″ and the end E_(serif) is less than D_(min), removing the element (E_(serif),0) from the set Ms; (i) searching for a unworkable element for all elements of the set Ms; and (j) when no unworkable element is found for all elements of the set Ms, defining first components of elements in the set Ms as fragmentation points for the segment S.

In an additional exemplary aspect of the present invention, a method for performing mask edge fragmentation of an integrated circuit design edge may include the following steps: (a) making initial edge fragmentation of an IC design edge; (b) performing an aerial image calculation of the IC design edge; (c) building process intensity profiles at ideal edge positions along the IC design edge; (d) selecting new fragmentation points for the IC design edge; and (e) changing edge fragmentation of the IC design edge.

It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention as claimed. The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate an embodiment of the invention and together with the general description, serve to explain the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

The numerous advantages of the present invention may be better understood by those skilled in the art by reference to the accompanying figures in which:

FIG. 1 illustrates a flowchart showing an exemplary method for optimizing fragmentation of boundaries for optical proximity correction (OPC) purposes in accordance with the present invention;

FIG. 2 shows an exemplary segment of an IC boundary and its neighborhood;

FIG. 3 shows exemplary segment ends and beginning and end serif points on the segment shown in FIG. 2 in accordance with the present invention;

FIG. 4 shows exemplary projection points on the segment shown in FIG. 3 in accordance with the present invention;

FIG. 5 shows the result after the projection points too close to segments ends are removed from the segment shown in FIG. 4 in accordance with the present invention;

FIG. 6 shows the result after the beginning serif point and the end serif point are removed from the segment shown in FIG. 5 in accordance with the present invention;

FIG. 7 shows the result after an unworkable point is removed from the segment shown in FIG. 6 in accordance with the present invention;

FIG. 8 shows fragmentation points after all unworkable points are removed from the segment shown in FIG. 6 in accordance with the present invention;

FIG. 9 is a flowchart showing an exemplary method for performing mask edge fragmentation in accordance with the present invention; and

FIG. 10 is an illustration useful in explaining the steps illustrated in FIG. 9.

DETAILED DESCRIPTION OF THE INVENTION

Reference will now be made in detail to the presently preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings.

Referring first to FIG. 1, a flowchart showing an exemplary method or process 100 for optimizing fragmentation of boundaries for optical proximity correction (OPC) purposes in accordance with the present invention is shown. The process 100 may start with step 102 in which a segment of an IC boundary and the IC boundary's neighborhood are provided. For example, a segment S of an IC boundary may be provided. The segment S may have two ends: B and E. A serif size for the segment S may be denoted as D_(serif), and a minimal allowed distance between any two fragmentation points on the segment S may be denoted as D_(min).

Then, in step 104, both ends of the segment may be placed into a set Ms and, when the length of the segment is not less than (D_(min)+2·D_(serif)), both a beginning serif point and an end serif point may be set on the segment and may also be placed into the set Ms. The element of the set Ms may take the form of a pair (P_(i), D_(i)), where a first component P_(i) is a point on the segment, and a second component D_(i) is a numeric value.

In the case of the segment S, elements (B,0) and (E,0) may be added to the set Ms. When the length of the segment S is not less than (D_(min)+2·D_(serif)), a beginning serif point B_(serif) may be denoted as a point which lies on the segment S with a distance between B and B_(serif) being equal to D_(serif), an end serif point E_(serif) may be denoted as a point which lies on the segment S with a distance between E and E_(serif) being equal to D_(serif), and elements (B_(serif),0) and (E_(serif),0) may be added to the set Ms.

In step 106, all vertices other than the segment ends may be projected to the segment, and when a projection point lies on the segment, the projection point may be added to the set Ms. In the case of the segment S, the projection of each vertex of the IC boundary and its neighborhood may define a distance from the vertex to the segment S. The distance from a vertex A to the segment S may be denoted as D_(A) and the corresponding projection point may be denoted as P_(A). When P_(A) lies on the segment S, the element (P_(A), D_(A)) may be added to the set Ms. Thus, in the case of the segment S, after the step 106, the set Ms may include the elements (B,0) and (E,0), the elements (B_(serif),0) and (E_(serif),0) (if applicable), and one or more elements (P_(A), D_(A)) (if applicable). In the following steps of the process 100, fragmentation points of the segment S may be selected from the set Ms.

In step 108, points too close to the segment ends may be removed from the set Ms. In the case of the segment S, if an element (P_(i), D_(i)) (other than B and E) of the set Ms is such that a distance between P_(i) and B or between P_(i) and E is less than D_(min), the element (P_(i), D_(i)) may be deleted from the set Ms.

Next, in step 110, an inquiry of whether a beginning serif point and an end serif point have been set on the segment may be performed. If the answer is no, the process 100 may proceed to step 114; if the answer is yes, the process 100 may proceed to step 112.

In the step 112, the beginning serif point and the end serif point may be removed from the set Ms. In the case of the segment S, if an element (P_(i), D_(i)) of the set Ms is such that the point P_(i) lies between B and B_(serif), and if another element (P_(i)′, D_(i)′) of the set Ms is such that a distance between P_(i)′ and B_(serif) is less than D_(min), the element (B_(serif),0) may be removed from the set Ms. Similarly, in the case of the segment S, if an element (P_(i), D_(i)) of the set Ms is such that the point P_(i) lies between E and E_(serif), and if another element (P_(i)′, D_(i)′) of the set Ms is such that a distance between P_(i)′ and E_(serif) is less than D_(min), the element (E_(serif),0) may be removed from the set Ms.

Next, in the step 114, a search for a “unworkable element” for all elements (except the segment ends) of the set Ms may be performed.

In the case of the segment S, in step 114-1, an element (P₁, D₁) of the set Ms may be selected, where the point P₁ is closest to the segment end B (but not B). If another element (P_(i), D_(i)) of the set Ms is such that a distance between P₁ and P_(i) is less than D_(min), then the element (P₁, D₁) may be marked as a “unworkable element,” this distance may be denoted as D_(unworkable), and the distance D₁ may be denoted as D_(unworkable) ^(priority). Then, in step 114-2, an element (P₂, D₂) of the set Ms may be selected, where the point P₂ is closest to the point P₁ and the element (P₂, D₂) differs from the elements (B,0), (E,0) and (P₁, D₁). If another element (P_(i), D_(i)) of the set Ms is such that a distance between P₂ and P_(i) is less than D_(unworkable) or such that a distance between P₂ and P_(i) is equal to D_(unworkable), but D₂ is greater than D_(unworkable) ^(priority), then the element (P₂, D₂) may be marked as a “unworkable element,” this distance may be denoted as D_(unworkable), and the distance D₂ may be denoted as D_(unworkable) ^(priority). Next, an element (P₃, D₃) of the set Ms may be selected, where the point P₃ is closest to the point P₂ and the element (P₃, D₃) differs from the elements (B,0), (E,0), (P₁, D₁), and (P₂, D₂). Then the step 114-2 may be repeated. The step 114 may be performed for all elements of the set Ms except the elements (B,0) and (E,0).

Then in step 116, an inquiry of whether a unworkable element has been found may be performed. If the answer is yes, the last marked unworkable element may be deleted from the set Ms in step 118, and the process 100 returns to the step 114; if the answer is no (i.e., no element of the set Ms has been marked as “unworkable element”), then the first components of the elements of the set Ms may be defined as fragmentation points for the segment.

FIGS. 2 through 8 show the results after various steps of the present method are performed on an exemplary segment S of an IC boundary in accordance with an exemplary embodiment of the present invention. FIG. 2 shows an exemplary segment S of an IC boundary and its neighborhood. FIG. 3 shows exemplary segment ends B and E and a beginning serif point B_(serif) and an end serif point E_(serif) on the segment S shown in FIG. 2 in accordance with the present invention. FIG. 4 shows exemplary projection points on the segment S shown in FIG. 3 in accordance with the present invention. FIG. 5 shows the result after the projection points too close to the segment ends B and E are removed from the segment S shown in FIG. 4 in accordance with the present invention. FIG. 6 shows the result after the beginning serif point B_(serif) and the end serif point E_(serif) are removed from the segment S shown in FIG. 5 in accordance with the present invention. FIG. 7 shows the result after an unworkable point is removed from the segment S shown in FIG. 6 in accordance with the present invention. FIG. 8 shows fragmentation points after all unworkable points are removed from the segment S shown in FIG. 6 in accordance with the present invention.

It is understood that the segment S shown in FIGS. 2 through 8 is exemplary only and not intended as a structural limitation to the present invention. Those of ordinary skill in the art will understand that the present invention may be applied to various segments of an IC boundary without departing from the scope and spirit of the present invention.

Referring now to FIG. 9, a flowchart showing an exemplary method or process 900 for performing mask edge fragmentation in accordance with the present invention is shown. The process 900 may start with step 902 in which initial edge fragmentation is performed and a number i_(number) is given a value “zero” (i_(number)=0), where i_(number) is the number of iterations performed. In a preferred embodiment, initial edge fragmentation is performed based on the projection of vertices of the design's boundaries, as shown in FIG. 1. Aerial image calculation or process intensity calculation may be performed 904. For example, the process intensity calculation may be performed as:

${I\left( {x,\; y,\;\overset{\rightarrow}{a}} \right)}\; = \;{{\frac{1}{I_{0}}{\int{\int{J\left( {x_{u},\; y_{u}} \right)}}}}❘{{E\left( {x,y,\; x_{u},\; y_{u},\;\overset{\rightarrow}{a}} \right)}❘^{2}{{\mathbb{d}x_{u}}{\mathbb{d}y_{u}}}}}$ where I₀ is open frame intensity; and J(x_(u),y_(u)) is the intensity distribution at the source surface.

When i_(number) is less than a pre-set value I₀, in step 906 intensity iterations for OPC process may be performed, and i_(number) is increased by 1. In a preferred embodiment, intensity iterations for OPC process may be performed as shown in U.S. patent application Ser. No. 09/879,664, entitled “Mask Correction for Photolithographic Processes”, filed Jun. 12, 2001. The result of the step 906 is an OPC decision close to the optimal one. Then the process 900 returns to the step 904.

When i_(number) is greater than the pre-set value I₀, in step 914 iterations for OPC process may be performed, and i_(number) is increased by 1. The step 914 may be preferably the same as the step 906. Then the process 900 returns to the step 904.

When i_(number) is equal to the pre-set value I₀, process intensity profiles at ideal edge positions may be built 908. The step 908 may be realized by calculation of process intensity values at the set of edge control points, which are the control points for the cost function of the iteration process (see, e.g., FIG. 10). A region of intensity sign changing may be defined as follows:

-   -   a) if Δ_(i)=I(p_(i))−C⁰>0 and Δ_(i+1)=I(p_(i+1))−C⁰<0, i=1, . .         . , P_(edge)−1, then the (p_(i), p_(i+1)) is the sign changing         region of the edge;     -   b) if Δ_(i)=I(p_(i))−C⁰<0 and Δ_(i+1)=I(p_(i+1))−C⁰>0, i=1, . .         . , P_(edge)−1, then the (p_(i), p_(i+1)) is the sign changing         region of the edge; and     -   c) if I(p_(i−1))<0, I(p_(i))=0 and I(p_(i+1))>0, or if         I(p_(i−1))>0, I(p_(i))=0 and I(p_(i+1))<0, i=1, . . . ,         P_(edge)−1, then p_(i) is the sign changing point,         where I(p_(i)) is the process intensity value at the i-th point         on the edge; C⁰ is the desired intensity value (cutline of the         aerial image contour); and P_(edge) is the number of control         points on the edge.

When a distance between control points is small (e.g., 0.1-0.3 of wavelength), the curve of the light intensity along the edge between points p_(i) and p_(i+1) may be presumed to change linearly. Thus, for the foregoing cases a) and b), linear approximation may be used for a distance between a sign changing point and the point p_(i):

$\bigtriangleup\; = \;\frac{\left| {{I\left( p_{i} \right)} - C^{0}} \middle| {\cdot {detlaP}} \right.}{\left| {{I\left( p_{i} \right)} - C^{0}} \middle| {+ \left| {{I\left( p_{i + 1} \right)} - C^{0}} \right|} \right.}$ where deltaP is the distance between control points p_(i) and p_(i+1) along the segment. Thus, new fragmentation points corresponding to the new design process intensity may be found. These new points may be added to the list of fragmentation points for the segment.

New fragmentation points may be selected from the list of fragmentation points for the segment 910. Denote the minimal allowed distance between the fragmentation points as D_(min). It is noted that this distance D_(min) is chosen so that the distance between any pair of the points are greater than D_(min). For each new point added to the list in the step 908, distances between this point and its neighbors may be checked. If a distance between this point and one neighbor point is less than D_(min), the neighbor point need be deleted from the list. As a result, the list of fragmentation points for the segment may define the fragmentation points for the edge. Then, in step 912, edge fragmentation is changed and i_(number) is increased by 1. Next, the process 900 returns to the step 904.

It is to be noted that the above described embodiments according to the present invention may be conveniently implemented using conventional general purpose digital computers programmed according to the teachings of the present specification, as will be apparent to those skilled in the computer art. Appropriate software coding may readily be prepared by skilled programmers based on the teachings of the present disclosure, as will be apparent to those skilled in the software art.

It is to be understood that the present invention may be conveniently implemented in forms of software package. Such a software package may be a computer program product which employs a storage medium including stored computer code which is used to program a computer to perform the disclosed function and process of the present invention. The storage medium may include, but is not limited to, any type of conventional floppy disks, optical disks, CD-ROMS, magneto-optical disks, ROMs, RAMs, EPROMs, EEPROMs, magnetic or optical cards, or any other suitable media for storing electronic instructions.

It is understood that the specific order or hierarchy of steps in the processes disclosed is an example of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged while remaining within the scope of the present invention. The accompanying method claims present elements of the various steps in a sample order, and are not meant to be limited to the specific order or hierarchy presented.

It is believed that the present invention and many of its attendant advantages will be understood by the foregoing description. It is also believed that it will be apparent that various changes may be made in the form, construction and arrangement of the components thereof without departing from the scope and spirit of the invention or without sacrificing all of its material advantages. The form herein before described being merely an explanatory embodiment thereof, it is the intention of the following claims to encompass and include such changes. 

1. A method for performing mask edge fragmentation of an integrated circuit design edge, comprising steps of: (a) making initial edge fragmentation of an IC design edge; (b) performing a process intensity of said IC design edge; (c) building process intensity profiles at ideal edge positions along said IC design edge; said building including: (c1) defining a sign changing region of said IC design edge as follows: (c11) when Δ_(i)=I(p_(i))−C⁰>0 and Δ_(i+1)=I(p_(i+1))−C⁰<0, i=1, . . . , P_(edge)−1, then (p_(i), p_(i+1)) is said sign changing region of said IC design edge; (c12) when Δ_(i)=I(p_(i))−C⁰<0 and Δ_(i+1)=I(p_(i+1))−C⁰>0, i=1, . . . , P_(edge) −1, then (p_(i), p_(i+1)) is said sign changing region of said IC design edge; and (c13) when I(p_(i−1))<0, I(p_(i))=0 and I(p_(i+1))>0, or when I(p_(i)) >0, I(p_(i))=0 and I(p_(i+1))<0, i=1, . . . , P_(edge)−1, then p_(i) is a sign changing point, wherein I(p_(i)) is a process intensity value at an i-th point on said IC design edge; C⁰ is a desired intensity value (cutline of an aerial image contour); and P_(edge) is a number of control points on said IC design edge; (c2) adding new fragmentation points corresponding to a new design process intensity of said IC design edge to a list of fragmentation points of said IC design edge; (d) selecting new fragmentation points for said IC design edge; and (e) changing edge fragmentation of said IC design edge.
 2. The method of claim 1, wherein said step (d) comprising: (d1) for one of said new fragmentation points, checking a distance between said one of said new fragmentation points and a neighbor point; and (d2) when said distance between said one of said new fragmentation points and said neighbor point is less than a predetermined value, deleting said neighbor point from said list.
 3. The method of claim 2, wherein said step (e) is performed based on said list.
 4. A computer-readable medium having computer-executable instructions for performing a method for performing mask edge fragmentation of an integrated circuit design edge, said method comprising steps of: (a) making initial edge fragmentation of an IC design edge; (b) performing a process intensity of said IC design edge; (c) building process intensity profiles at ideal edge positions along said IC design edge; said building including: (c1) defining a sign changing region of said IC design edge as follows: (c11) when Δ=I(p_(i))−C⁰>0 and Δ_(i+1)=I(p_(i+1))−C⁰<0, i=1, . . . , P_(edge)−1, then (p_(i), p_(i+1)) is said sign changing region of said IC design edge; (c12) when Δ_(i)=I(p_(i))−C⁰<0 and Δ_(i+1)=I(p_(i+1))−C⁰>0, i=1, . . . , P_(edge)−1, then (p_(i), p_(i+1)) is said sign changing region of said IC design edge; and (c13) when I(p_(i−1))<0, I(p_(i))=0 and I(p_(i+1))>0, or when I(p_(i+1)) >0, I(p_(i))=0 and I(p_(i+1))<0, i=1, . . . , P_(edge)−1, then p_(i) is a sign changing point, said I(p_(i)) is a process intensity value at an i-th point on said IC design edge; C⁰ is a desired intensity value (cutline of an aerial image contour); and P_(edge) is a number of control points on said IC design edge; and (c2) adding new fragmentation points corresponding to a new design process intensity of said IC design edge to a list of fragmentation points of said IC design edge; (d) selecting new fragmentation points for said IC design edge; and (e) changing edge fragmentation of said IC design edge.
 5. The computer-readable medium of claim 4, wherein said step (d) comprising: (d1) for one of said new fragmentation points, checking a distance between said one of said new fragmentation points and a neighbor point; and (d2) when said distance between said one of said new fragmentation points and said neighbor point is less than a predetermined value, deleting said neighbor point from said list.
 6. The computer-readable medium of claim 5, wherein said step (e) is performed based on said list. 